Meso-scale Finite Element Model Research Articles

A Mesoscale Comparative Analysis of the Elastic Modulus in Rock-Filled Concrete for Structural Applications

Rock-filled concrete (RFC) is an advanced construction material that integrates high-performance self-compacting concrete (HSCC) with large rocks exceeding 300 mm, providing advantages such as reduced hydration heat and increased construction processes. The elastic modulus of RFC is a critical parameter that directly influences its structural performance, making it vital for modern construction applications that require strength and stiffness. However, there is a scientific gap in understanding the effects of rock size, shape, arrangement, and volumetric ratio on this parameter. This study investigates these factors using mesoscale finite element models (FEMs) with spherical and polyhedral rocks. The results reveal that polyhedral rocks increase the elastic modulus compared to spherical rocks, enhancing RFC’s load-bearing capacity. Additionally, a 5% increase in the elastic modulus was observed when the rockfill ratio was increased from 50% to 60%, demonstrating a direct correlation between rock volume and mechanical performance. Furthermore, the elastic modulus rises significantly in the early stages of placement, followed by a gradual increase over time. Optimal rock sizes and a balanced mix of rock shapes allow for improved concrete flow and mechanical properties, making RFC a highly efficient material for construction. These findings offer valuable insights for designers and engineers looking to optimize RFC for structural applications.

Revealing the failure mechanism of 2D triaxially braided composites under off-axial tension through mesoscale simulations

The external load angle is known to have a significant influence on the mechanical behavior of two-dimensional triaxially braided composites (2DTBCs). However, the experimental data for 2DTBCs under off-axial loading provide limited information for understanding the failure mechanisms. In this study, a comprehensive mesoscale finite element (FE) model for simulating 2DTBC specimens was established to evaluate the mechanical responses and damage characteristics when off-axial tensile loads are applied. The FE model effectively captured the mechanical response at five distinct angles (0°, 30°, 45°, 60°, and 90°) and revealed the evolving patterns of failure behavior, damage morphology, and out-of-plane deformation mechanisms corresponding to the different loading angles. The findings indicate that, when the external load aligns with the axial fiber bundle direction, the primary failure mechanism involves the fracture of load-bearing fiber bundles. In contrast, deviations from the axial loading direction resulted in failure that was primarily due to the undulation of the bias fiber bundles, resulting in a loading angle–dependent warping at the edge of the specimen due to local shear stress concentration. The findings of this study provide valuable insights that can inform the design of structures with improved application.

Meso-scale Study of Bond Behavior between Ribbed Steel Rebar and Fiber-reinforced Cementitious Composite Considering Rebar Rib Geometry

This study aims to develop a meso-scale finite element approach to investigate the pull-out behavior of ribbed steel rebar and fiber-reinforced cement composites. We considered separately the three phases of steel fibers, cement composite matrix, and rebar within the meso-scale finite element model. A random distribution of fibers was generated in the matrix based on the geometric characteristics of the fibers and their volume fraction. By employing the interfacial transition zone (ITZ) model, the interaction between rebar and fibers with cement composite was simulated. Experimental pull-out tests were conducted to determine the parameters of the model. A meso-scale finite element model was validated and the effect of rebar diameter and fiber volume fraction on the bond behavior of rebar with fiber-reinforced cement composites was examined. In accordance with the experimental results, the bond-slip curve obtained with the meso-scale finite element model can be divided into five areas: non-slip, slight slip, splitting, decreasing, and residual. Additionally, it can be observed that fiber-free cement composites fail by splitting, whereas specimens containing fibers fail by sliding. This numerical model is therefore able to predict and estimate the influence of a variety of parameters on the pull-out response between fiber-reinforced cement composite and ribbed bar and failure mechanisms without the need for expensive and time-consuming testing.

Experimental and numerical study on moisture diffusion behavior of 3D woven composite

In this paper, a meso-scale finite element model was established to investigate the moisture diffusion in 3D woven carbon fiber reinforced composites (CFRCs), and to analyze the internal stresses caused by hygroscopic deformation. To quickly obtain the mesoscopic moisture diffusion parameters, an optimization procedure that fitted the simulation results to the experimental results was implemented to achieve automatic inverse identification of each parameter. The homogenized analytical models for describing the moisture diffusion in yarns and resin, specifically Fick’s and Langmuir-type models, were evaluated. The results indicated that Langmuir-type model provided more accurate fitting results, attributed to its consideration of anomalous moisture absorption. Furthermore, the internal stress induced by moisture absorption was analyzed for composites aging at 82 °C over different time intervals. The accumulation of hygroscopic stress was observed at the intersection of warp and weft yarns, as well as at the interface between the weft yarn and matrix.

Efficient Simulation of the Laser-Based Powder Bed Fusion Process Demonstrated on Open Lattice Materials Fabrication

Strut-based or open lattice materials are a category of advanced materials used in medical and aerospace applications due to their properties, such as high strength-to-weight ratio and energy absorption capability. The most prominent method for the fabrication of lattice materials is the Laser-based Powder Bed Fusion (L-PBF) additive manufacturing (AM) process, due to its ability to produce parts of complex geometries. The current work presents an efficient meso-scale finite element (FE) modeling methodology of the L-PBF process demonstrated in the fabrication of body-centered cubic (BCC) lattice materials. The modeling efficiency is gained through an adaptive mesh refinement technique, which results in accurate and efficient prediction of the temperature field during the process evolution. To examine the efficiency of the modeling method, the computational time is compared with that of a conventional FE simulation, based on the element and birth technique. The temperature history difference between the two approaches is minor but the adaptive mesh modeling requires only a small portion of the simulation time of the conventional model. In addition, the computational results present a good correlation with the available experimental measurements for various process parameters validating the presented efficient method.

Direct validation of 3D meso-scale fracture modelling of UHPFRC by in-situ micro X-ray CT wedge-split tests and parametric studies

3D meso-scale finite element models of ultra high performance fibre reinforced concrete (UHPFRC) based on in-situ micro X-ray Computed Tomography (CT) images are developed and validated in this study. The CT images at 16.9 μm voxel resolution from a progressive wedge-split test were converted into meso-scale 3D tetrahedron meshes. The short fibres, embedded in the mortar matrix, were modelled by truss elements with equivalent elastoplastic constitutive laws transformed from single fibre pullout load–displacement curves, so as to indirectly model the fibre–matrix interfaces. A concrete damage plasticity model was used to simulate damage and fracture in the mortar. The simulated load–displacement curves, final crack patterns, and load-crack opening curves were found in good agreement with the in-situ CT test results, and the non-vertical crack path was significantly affected by the overall orientation of fibres bridging the crack. Further simulations with all the fibres perpendicular to the tensile splitting direction showed that the peak load and fracture energy increased by 42 % and 45 % respectively from 1 % to 3 % fibre volume fraction. This indicates the need to optimize the fibre orientation for best mechanical performance according to the loading conditions.

Progressive damage modeling in open hole composite laminates with ultrasound-informed drilling-induced delamination

Insertion of fasteners, often used in aerospace and automotive industries, requires drilling that induces non-uniform delamination between lamina of a carbon fiber reinforced plastic (CFRP). Understanding the effect of drilling-induced delamination on the mechanical performance and associated damage mechanisms (progressive damage and failure) is critical to ensure joining integrity. The present work develops an ultrasound testing (UT) method to quantify the drilling-induced delamination at each individual ply interface for CFRP laminates. We then develop a mesoscale finite element (FE) model of an open hole tension specimen by incorporating the UT-obtained drilling-induced delamination at each interface. This delamination is modeled using cohesive zone elements with a bilinear traction-separation law with progressive damage in each ply modeled using the 3D Hashin along with a progressive damage model. Our FE model, with UT-informed delamination, accurately predicts experimental observations of the stress concentration around the hole, damage progression, and open hole tension strength.

Effect of steel fibre with different orientations on mechanical properties of 3D-printed steel-fibre reinforced concrete: Mesoscale finite element analysis

It is widely recognized that steel fibres exhibit directional distribution during the preparation of 3D-printed steel fibre reinforced concrete (SFRC). The degree of fibre orientation varies due to several factors, such as nozzle size and layer height. This variation in fibre orientation range may result in different mechanical performance exhibited by 3D-printed SFRC at hardened state. To explore the relationship between steel fibre orientation and the mechanical properties of 3D-printed SFRC at hardened state, this study firstly establishes three-dimensional mesoscale finite element models based on the distribution of fibres in 3D-printed SFRC. The steel fibre and matrix work together through a mechanism for fluid-structure interaction between models. Then, compares the simulation results with experimental data to verify the accuracy of the models. After that, different steel fibre distribution orientations were set, and parametric analysis was conducted for the compressive and tensile loading conditions to explore the effects of fibre orientation on the damage mode and strength of 3D-printed SFRC. The results indicate that 3D-printed SFRC exhibits different damage modes with varying steel fibre orientation ranges. Additionally, the strength of 3D-printed SFRC varies in steel fibre orientation range and exhibits anisotropic characteristics. This study provides a theoretical basis for improving and controlling the performance of 3D-printed SFRC in future engineering applications.

Tensile failure of open-hole composite laminates with yarn gaps: Experimental and numerical study

The tensile mechanical behavior and failure mechanism of multidirectional carbon-fiber-fabric-reinforced open-hole composite laminates were investigated in this study. Using digital image correlation (DIC) technology, test specimens were subjected to quasi-static tensile tests to determine their macroscale mechanical properties. An analytical framework was developed to predict the tensile properties, damage evolution, and failure mechanisms of the open-hole composite laminates. Two types of finite element (FE) models: mesoscale model and macroscale-equivalent model, were established. The mesoscale model considers the coupling effect of the yarn gaps and central circular hole. An Abaqus subroutine was written to introduce the Hashin failure criterion, considering the stiffness degradation. The fracture morphology was examined by scanning electron microscopy (SEM) to determine the failure mechanism of the specimens. The results show that the average ultimate load of the specimens is 27.2 kN. The errors predicted by the macroscale-equivalent and mesoscale models are 5.5 % and 1.5 %, respectively. The mesoscale FE model accurately simulated the damage evolution process of each layer under the coupling effect of the yarn gaps and central circular hole. The simulation results and SEM images showed the different failure modes of the fiber layers at different angles.

Formation of field-induced breakdown precursors on metallic electrode surfaces

Understanding the underlying factors responsible for higher-than-anticipated local field enhancements required to trigger vacuum breakdown on pristine metal surfaces is crucial for the development of devices capable of withstanding intense operational fields. In this study, we investigate the behavior of nominally flat copper electrode surfaces exposed to electric fields of hundreds of MV/m. Our novel approach considers curvature-driven diffusion processes to elucidate the formation of sharp breakdown precursors. To do so, we develop a mesoscale finite element model that accounts for driving forces arising from both electrostatic and surface-tension-induced contributions to the free energy. Our findings reveal a dual influence: surface tension tends to mitigate local curvature, while the electric field drives mass transport toward regions of high local field density. This phenomenon can trigger the growth of sharper protrusions, ultimately leading to a rapid enhancement of local fields and, consequently, to a runaway growth instability. We delineate supercritical and subcritical regimes across a range of initial surface roughness. Our numerical results are in qualitative agreement with experimentally reported data, indicating the potential practical relevance of field-driven diffusion in the formation of breakdown precursors.

A 3D Meso-Scale Model and Numerical Uniaxial Compression Tests on Concrete with the Consideration of the Friction Effect.

Achieving the real mechanical performance of construction materials is significantly important for the design and engineering of structures. However, previous researchers have shown that contact friction performs an important role in the results of uniaxial compression tests. Strong discreteness generally appears in concrete-like construction materials due to the random distribution of the components. A numerical meso-scale finite-element (FE) method provides the possibility of generating an ideal material with the same component percentages and distribution. Thus, a well-designed meso-FE model was employed to investigate the effect of friction on the mechanical behavior and failure characteristics of concrete under uniaxial compression loading. The results showed that the mechanical behavior and failure profiles of the simulation matched well with the experimental results. Based on this model, the effect of friction was determined by changing the contact friction coefficient from 0.0 to 0.7. It was found that frictional contact had a slight influence on the elastic compressive mechanical behavior of concrete. However, the nonlinear hardening behavior of the stress-strain curves showed a fairly strong relationship with the frictional contact. The final failure profiles of the experiments showed a "sand-glass" shape that might be expected to result from the contact friction. Thus, the numerical meso-scale FE model showed that contact friction had a significant influence on both the mechanical performance and the failure profiles of concrete.

Analysis of coupled thermo-mechanical response and damage behaviour of curved ramp bridge deck pavement using a 3D multiscale method

A three-dimensional (3D) multiscale modelling approach was developed in this study, which considers a two-way coupling of material properties and mechanical responses between macroscale (pavement level) and mesoscale (mixture level) finite element (FE) models. Both thermal and mechanical properties at the two scales were linked through a homogenisation method, and the boundary response was transferred from the macroscopic target element to the mesoscale model using a mapping procedure. The results show that seasonal temperature variations have a significant effect on the coupled thermo-mechanical response within bridge deck pavement. In winter, the deck pavement is subject to tensile stresses, the maximum values of which mainly occur at the tire edges and the dual-tire clearance centre; while the deck pavement experiences compressive stresses in summer, and the stress difference within the asphalt concrete layer increases with the temperature.

Effective mechanisms responsible for increased strength and fracture strain of carbon fiber-reinforced plastic/steel hybrid laminates

The tensile properties of carbon fiber-reinforced plastic (CFRP)/steel laminates have been observed to exceed the expected values predicted by the rule of mixture. While the CFRP/steel laminate is expected to fail at the failure strain of the CFRP lamina, it was observed that hybridization with a steel lamina improves the failure strain. This study investigates numerically and analytically the roles of each influential mechanism responsible for this enhancement, including the thermal residual strain, bridging effect, effect of compressive transverse stress on CFRP layers, and effect of tensile transverse stress on steel layers. To assess these mechanisms, multiple finite-element and analytical models were developed. A mesoscale finite-element model was proposed, which uses novel random fiber distribution algorithm capable of reproducing random fibers with high fiber volume fractions exceeding 65%. Rather than the meso-scale model, macro finite-element models and analytical relationships were developed to assess each hybrid mechanism. Analysis showed 6% increase of the failure strain due to thermal effect and up to 11% increase of strength due to multiaxial stress in steel layer. The results of this study contribute to a deeper understanding of the role of each phenomenon that contributes to improved tensile properties in hybrid CFRP/metal laminates.

Numerical mapping relationship between process parameters and mechanical properties of unidirectional carbon/carbon composites

This paper proposes an innovative algorithm derived from the isothermal chemical infiltration process to generate quasi-real microstructures of unidirectional carbon/carbon composites. This algorithm, which can predict the relationship between the composite density and infiltration time, is termed the isothermal chemical infiltration algorithm. To further evaluate the relationship between the process parameters and the mechanical properties, a mesoscale finite element model of the unidirectional carbon/carbon composite is established based on the isothermal chemical infiltration algorithm. After validation, the developed numerical model is employed to study the effects of the infiltration time, pressure, and temperature on the effective mechanical properties. The results show that the transverse modulus and tensile strength increase with an increase in the infiltration time, pressure, and temperature, with the effect of temperature being the most significant. In parallel, it is revealed that the complete failure of unidirectional carbon/carbon composites results from interfacial debonding and propagation of multiple cracks during transverse tension. The proposed model has potential applications in the process design and optimization of high-performance carbon/carbon composites.

Investigation of flexural behavior of crimped SMA fiber-reinforced mortar beams through experimental study and mesoscale finite element modeling

This study examined the influence of the volume fraction, distribution, and orientation of crimped shape memory alloy (SMA) fibers on the flexural behavior of mortar beams through experimental tests and mesoscale finite element model (M-FEM). In the experimental testing, five groups of beams were cast, including one group with no fibers and two groups, each having a fiber volume fraction of 1.0% and 1.5%. One group of beams with a fiber volume fraction of 1.0% and 1.5% were heated to induce the shape memory effect (SME). The beams were tested by a three-point bending test to estimate their flexural capacity. In the FE analysis, the three-dimensional M-FEM of beams with different fiber volume fractions (from 0.5% to 2.0%) was developed and implemented using Python scripting and computed with the ABAQUS environment. The FE analysis results matched well with experimental data. The maximum discrepancies are 6.5% in ultimate load and 4.5% in the corresponding displacement. Furthermore, increasing SMA fiber volume fractions up to 1.5% enhanced flexural strength in SMA fiber-reinforced mortar beams, while exceeding this fraction led to negative effects due to debonding and slippage from steel reinforcement, resulting in reduced load capacity. The heated beams to induced prestressing exhibited superior performance with an ultimate load increase of over 15.0% compared to nonheated beams. Finally, this study recommends using M-FEM to investigate the SMA fiber’s reinforced structures.

Evaluation of compressive strength of Euphorbia tortilis cactus infused M25 concrete by using ABAQUS under static load

This research presents a novel approach for numerically analyzing concrete with Euphorbia Tortilis Cactus (ETC) to determine its compressive strength. Mesoscale finite element (FE) models were developed, incorporating the mechanical properties of different concrete components. Two sets of concrete specimens with varying ETC content were studied. ABAQUS's explicit dynamics solver was employed for the analysis, and the computed compressive strengths closely matched the experimental data, with deviations of 1.2% and 0.96% (affecting elasticity and strength) for the concrete sets with and without ETC, respectively. The study demonstrates the accuracy and effectiveness of this approach as a quality control tool for concrete constructions, affirming the applicability of ABAQUS for predicting concrete strength.

High-fidelity prediction and temperature-rise mechanism for low-velocity impact of triaxially braided composites

An elastoplastic mechanical-thermal constitutive model was integrated into the development of a mesoscale finite element model. This model aimed to analyze the temperature rise phenomenon and failure behavior of composites under impact loading conditions. Triaxially braided carbon/epoxy composite specimens were subjected to low-velocity impact using a drop weight tester, and the temperature variations within the specimens were monitored using an infrared camera. The numerical predictions successfully reproduced the observed failure modes and accurately captured the temperature distribution. A numerical study was performed to explore the main factors of temperature rise, indicating that plastic work of pure matrix and fracture transformed energy of fiber tow are the primary sources of temperature rise. The transverse specimen was found to exhibit superior energy absorption capacity under high-energy impacts.

Mesoscale Modeling of Polymer Concrete Dynamic Properties.

There is a constant need to predict the dynamic properties of composite materials already at the design stage. A particularly attractive tool for achieving this goal is mesoscale finite element modeling. This paper presents the mesoscale modeling of the dynamic properties of polymer concrete. The method is based on finite element modeling and substructural identification. Substructural identification is a model updating technique based on frequency response functions. It enables the identification of model dynamic properties considering damping. The presented method is used to model the dynamic properties of a polymer concrete beam. In the first step, the mesoscale finite element model is built and then it is decoupled into substructures: a polymer matrix, aggregates, and an interfacial transition zone (ITZ). Next, the dynamic properties of the polymer matrix substructure are updated, and the model is reassembled. Then, second-stage updating takes place, which consists of determining the parameters of the aggregates and the ITZ. The use of substructural identification made it possible to determine the parameters of substructures that do not exist in an independent, isolated form like the ITZ. Moreover, it allows for determining the amount of damping that ITZ brings to the structure.

Experimental and numerical analyses of the effect of fibre content on the close-in blast performance of a UHPFRC beam

Limited research has been conducted on the influences of fiber content on close-in blasting characteristics for ultrahigh-performance fiber-reinforced concrete (UHPFRC) beams. This paper aims to address this knowledge gap through experimental and mesoscale numerical methods. Experiments were conducted on ten UHPFRC beams built with varying steel fiber volumetric fractions subjected to close-in explosive conditions. Additionally, this study considered other parameters, such as the longitudinal reinforcement type and ratio. In the case of UHPFRC beams featuring normal-strength longitudinal reinforcement of diameters Φ12, Φ16, and Φ20, a reduction in maximum displacement by magnitudes of 19.6%, 19.5%, and 17.4% was observed, respectively, as the volumetric fractions of fiber increased from 1.0% to 2.5%. In addition, increasing the longitudinal reinforcement ratio and using high-strength steel longitudinal reinforcement both significantly reduced the deformation characteristics and increase the blasting resistances of UHPFRC beams. However, the effects on the local crushing and spalling damage were not significant. A mesoscale finite element model, which considers the impacts of fiber parameters on UHPFRC beam behaviors, was also established and well correlated with the test findings. Nevertheless, parametric analyses were further conducted to examine the impacts of the steel fiber content and length and the hybrid effects of various types of microfibers and steel fibers on the blasting performance of UHPFRC beams.

A 3D cohesive‐frictional coupled interface model for mesoscale simulation of steel fibre‐reinforced concrete

AbstractA 3D mesoscale finite element modelling approach is developed for simulating complicated damage and fracture behaviour in steel fibre‐reinforced concrete (SFRC) with explicit modelling of fibre–matrix interfaces. In this approach, a new 3D four‐noded cohesive‐frictional coupled interface element is developed to model the nonlinear interfacial bond‐slip behaviour, supplemented by a kinematic multiple‐point‐constraint (kMPC) algorithm to simulate the wrapping effect of the mortar around the fibres. They are implemented as a user‐defined element (UEL) and a user‐defined MPC subroutine in ABAQUS, respectively. Three cohesive‐frictional constitutive relationships are proposed to describe the nonlinear bond‐slip behaviour of different fibre–matrix compositions. The new approach is validated by single fibre pullout tests, direct tensile tests and three‐point bending tests of SFRC specimens with randomly distributed fibres. The results show that the new approach is capable of effectively capturing typical failure mechanisms in SFRC, such as fibre yielding, matrix failure, and fibre–matrix debonding and slipping.